Today’s Puzzle:

How would I solve this puzzle? I would want to find a set of 12 consecutive numbers that were all positive and relatively small. Since there is an empty triangle near the right side of the puzzle, I would begin with the triangle on the bottom with a 4 in it and write 12 in a box above it. Then I would think and write 12 – 4 = 8 for the other box above the 4. My thinking would look like this:

• 12
• 12 – 4 = 8 (going to the right of the 12)
• 12 – 6 = 6 (going to the left of the 12)
• 6 + 7 = 13
• 13 – 6 = 7
• 7 – 2 = 5
• 5 + 5 = 10
• 10 + 5 = 15
• 15 – 6 = 9

So that the puzzle looks like this:

I would note that I’m missing the following numbers: 1, 2, 3, 4, 11, and 14, and would figure out which of those missing numbers fit in the last three squares. Because I have a 15, I would note that 15 – 12 = 3 and would subtract 3 from each square to get numbers from 1 to 12. Figuring out what belongs in the empty triangle won’t be difficult either.

Factors of 1790:

• 1790 is a composite number.
• Prime factorization: 1790 = 2 × 5 × 179.
• 1790 has no exponents greater than 1 in its prime factorization, so √1790 cannot be simplified.
• The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1790 has exactly 8 factors.
• The factors of 1790 are outlined with their factor pair partners in the graphic below.

More About the Number 1790:

1790 is the hypotenuse of a Pythagorean triple:
1074-1432-1790 which is (3-4-5) times 358.

1789 is 414 in base 21, but
1790 is 4I4 in base 19 because 4(19²) + 18(19) + 4(1) = 1790.